Predicting birth weight by multivariate functional principal component regressions

Functional data analysis (FDA) provides a powerful statistical framework for analyzing complex data, such as curves or functions, over high-dimensional domains. In this paper, we focus on functional predictor regression (scalar-on-function) models applied to the prediction of birth weight using maternal dietary patterns during pregnancy. Specifically, we analyze trajectories of nine components of the Alternative Healthy Eating Index (AHEI) as multivariate functional predictors. We adopt Multivariate Functional Principal Component Analysis (MVFPCA) to obtain low-dimensional, uncorrelated representations of the multivariate functional predictors through their FPC scores. Building on MVFPCA, we develop a novel multivariate functional principal component regression (MVFPCR) model to predict birth weight effectively. Our method accommodates various regression approaches, including linear and quantile regression, depending on the distribution of birth weights. Through simulation studies and the application to a fetal growth study dataset, we demonstrate the effectiveness of our proposed model in functional predictor regression.